Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+5y &= 6 \\ -2x+9y &= 8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = -9y+8$ Divide both sides by $-2$ to isolate $x$ $x = {\dfrac{9}{2}y - 4}$ Substitute this expression for $x$ in the first equation. $-2({\dfrac{9}{2}y - 4}) + 5y = 6$ $-9y + 8 + 5y = 6$ Simplify by combining terms, then solve for $y$ $-4y + 8 = 6$ $-4y = -2$ $y = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $y$ in the top equation. $-2x+5( \dfrac{1}{2}) = 6$ $-2x+\dfrac{5}{2} = 6$ $-2x = \dfrac{7}{2}$ $x = -\dfrac{7}{4}$ The solution is $\enspace x = -\dfrac{7}{4}, \enspace y = \dfrac{1}{2}$.